Date: Fri, 29 Oct 10 00:06:36 GMT Subject: math-ph daily 8 new + 6 crosses received by eprepget ------------------------------------------------------------------------------ ------------------------------------------------------------------------------ Send any comments regarding submissions directly to submitter. ------------------------------------------------------------------------------ Archives at http://arxiv.org/ To unsubscribe, e-mail To: math-ph@arXiv.org, Subject: cancel ------------------------------------------------------------------------------ received by eprepget from Wed 27 Oct 10 20:00:00 GMT to Thu 28 Oct 10 20:00:00 GMT ------------------------------------------------------------------------------ \\ arXiv:1010.5804 Date: Wed, 27 Oct 2010 20:46:16 GMT (30kb,D) Title: Tensor structure from scalar Feynman matroids Authors: Dirk Kreimer and Karen Yeats Categories: math-ph math.MP Comments: 11 pages MSC-class: 81T18 \\ We show how to interpret the scalar Feynman integrals which appear when reducing tensor integrals as scalar Feynman integrals coming from certain nice matroids. \\ ( http://arxiv.org/abs/1010.5804 , 30kb) ------------------------------------------------------------------------------ \\ arXiv:1010.5855 Date: Thu, 28 Oct 2010 04:22:42 GMT (10kb) Title: Critical phenomena in the Dyson hierarchical model and renormalization group Authors: Pavel Bleher Categories: math-ph math.MP Comments: 12 pages MSC-class: 82B28 (Primary) 82B27 (Secondary) \\ We review some results on the critical phenomena in the Dyson hierarchical model and renormalization group. \\ ( http://arxiv.org/abs/1010.5855 , 10kb) ------------------------------------------------------------------------------ \\ arXiv:1010.5859 Date: Thu, 28 Oct 2010 04:36:55 GMT (4kb) Title: Higher derived brackets Authors: Ezra Getzler Categories: math-ph math.MP MSC-class: 17B60, 17B63, 18G55, 53D17 \\ We show that there is a sequence of operations on the positively graded part of a differential graded algebra making it into an L-infinity algebra. The formulas for the higher brackets involve Bernoulli numbers. The construction generalizes the derived bracket for Poisson manifolds, and the Lie 2-algebra associated to a Courant algebroid constructed by Roytenberg and Weinstein. \\ ( http://arxiv.org/abs/1010.5859 , 4kb) ------------------------------------------------------------------------------ \\ arXiv:1010.5866 Date: Thu, 28 Oct 2010 06:02:12 GMT (14kb) Title: The Multicomponent KP Hierarchy: Differential Fay Identities and Lax Equations Authors: Lee-Peng Teo Categories: math-ph math.MP Comments: 19 pages \\ In this article, we show that four sets of differential Fay identities of an $N$-component KP hierarchy derived from the bilinear relation satisfied by the tau function of the hierarchy are sufficient to derive the auxiliary linear equations for the wave functions. From this, we derive the Lax representation for the $N$-component KP hierarchy, which are equations satisfied by some pseudodifferential operators with matrix coefficients. Besides the Lax equations with respect to the time variables proposed in \cite{2}, we also obtain a set of equations relating different charge sectors, which can be considered as a generalization of the modified KP hierarchy proposed in \cite{3}. \\ ( http://arxiv.org/abs/1010.5866 , 14kb) ------------------------------------------------------------------------------ \\ arXiv:1010.5898 Date: Thu, 28 Oct 2010 09:09:36 GMT (12kb) Title: Quantum Mechanics as Asymptotics of Solutions of Generalized Kramers Equation Authors: E.M. Beniaminov Categories: math-ph math.MP Comments: 18 pages \\ We consider the process of diffusion scattering of a wave function given on the phase space. In this process the heat diffusion is considered only along momenta. We write down the modified Kramers equation describing this situation. In this model, the usual quantum description arises as asymptotics of this process for large values of resistance of the medium per unit of mass of particle. It is shown that in this case the process passes several stages. During the first short stage, the wave function goes to one of "stationary" values. At the second long stage, the wave function varies in the subspace of "stationary" states according to the Schrodinger equation. Further, dissipation of the process leads to decoherence, and any superposition of states goes to one of eigenstates of the Hamilton operator. At the last stage, the mixed state of heat equilibrium (the Gibbs state) arises due to the heat influence of the medium and the random transitions among the eigenstates of the Hamilton operator. Besides that, it is shown that, on the contrary, if the resistance of the medium per unit of mass of particle is small, then in the considered model, the density of distribution of probability $\rho =|\phi |^2$ satisfies the standard Liouville equation, as in classical statistical mechanics. \\ ( http://arxiv.org/abs/1010.5898 , 12kb) ------------------------------------------------------------------------------ \\ arXiv:1010.5925 Date: Thu, 28 Oct 2010 11:27:16 GMT (14kb) Title: On a certain class of semigroups of operators Authors: Paolo Aniello Categories: math-ph math.MP Comments: 11 pages \\ We define an interesting class of semigroups of operators in Banach spaces, namely, the randomly generated semigroups. This class contains as a remarkable subclass a special type of quantum dynamical semigroups introduced by Kossakowski in the early 1970s. Each randomly generated semigroup is associated, in a natural way, with a pair formed by a representation or an antirepresentation of a locally compact group in a Banach space and by a convolution semigroup of probability measures on this group. Examples of randomly generated semigroups having important applications in physics are briefly illustrated. \\ ( http://arxiv.org/abs/1010.5925 , 14kb) ------------------------------------------------------------------------------ \\ arXiv:1010.5945 Date: Thu, 28 Oct 2010 12:40:52 GMT (10kb) Title: Produits Gamma et vecteurs propres de matrices de Cartan Authors: V. Cohen-Aptel, V.Schechtman Categories: math-ph math.MP Comments: 17 pages \\ We propose a formula expressing Perron - Frobenius eigenvectors of Cartan matrices in terms of products of values of the Gamma function. \\ ( http://arxiv.org/abs/1010.5945 , 10kb) ------------------------------------------------------------------------------ \\ arXiv:1010.5981 Date: Thu, 28 Oct 2010 14:39:50 GMT (8kb) Title: Dirac Equation with Spin Symmetry for the Modified P\"oschl-Teller Potential in $D$-dimensions Authors: D. Agboola Categories: math-ph math.MP quant-ph Comments: 9 pages and 1table \\ We present solutions of the Dirac equation with spin symmetry for vector and scalar modified P\"oschl-Teller potential within framework of an approximation of the centrifugal term. The relativistic energy spectrum is obtained using the Nikiforov-Uvarov method and the two-component spinor wavefunctions are obtain are in terms of the Jacobi polynomials. It is found that there exist only positive-energy states for bound states under spin symmetry, and the energy levels increase with the dimension and the potential range parameter $\alpha$. \\ ( http://arxiv.org/abs/1010.5981 , 8kb) %-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%-%- ------------------------------------------------------------------------------ \\ arXiv:1007.4601 (*cross-listing*) Date: Tue, 27 Jul 2010 01:19:32 GMT (1145kb,D) Date (revised v2): Wed, 27 Oct 2010 23:15:24 GMT (1144kb,D) Title: Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes Authors: Beni Yoshida Categories: quant-ph cond-mat.str-el math-ph math.MP Comments: 101 pages, 30 figures, to appear in annals of physics \\ Searches for possible new quantum phases and classifications of quantum phases have been central problems in physics. Yet, they are indeed challenging problems due to the computational difficulties in analyzing quantum many-body systems and the lack of a general framework for classifications. While frustration-free Hamiltonians, which appear as fixed point Hamiltonians of renormalization group transformations, may serve as representatives of quantum phases, it is still difficult to analyze and classify quantum phases of arbitrary frustration-free Hamiltonians exhaustively. Here, we address these problems by sharpening our considerations to a certain subclass of frustration-free Hamiltonians, called stabilizer Hamiltonians, which have been actively studied in quantum information science. We propose a model of frustration-free Hamiltonians which covers a large class of physically realistic stabilizer Hamiltonians, constrained to only three physical conditions; the locality of interaction terms, translation symmetries and scale symmetries, meaning that the number of ground states does not grow with the system size. We show that quantum phases arising in two-dimensional models can be classified exactly through certain quantum coding theoretical operators, called logical operators, by proving that two models with topologically distinct shapes of logical operators are always separated by quantum phase transitions. \\ ( http://arxiv.org/abs/1007.4601 , 1144kb) ------------------------------------------------------------------------------ \\ arXiv:1010.5797 (*cross-listing*) Date: Wed, 27 Oct 2010 20:19:48 GMT (24kb) Title: Generalized Dirac bracket and the role of the Poincar\'e symmetry in the program of canonical quantization of fields 1 Authors: Marcin Ka\'zmierczak Categories: hep-th math-ph math.MP quant-ph \\ An elementary presentation of the methods for the canonical quantization of constraint systems with Fermi variables is given. The emphasis is on the subtleties of the construction of an appropriate classical bracket that could be consistently replaced by commutators or anti--commutators of operators, as required by canonical quantization procedure for bosonic and fermionic degrees of freedom respectively. I present a consequent canonical quantization of the Dirac field, in which the role of Poincar\'e invariance is made marginal. This simple example provides an introduction to the Poincar\'e--free quantization of spinor electrodynamics in the second part of the paper. \\ ( http://arxiv.org/abs/1010.5797 , 24kb) ------------------------------------------------------------------------------ \\ arXiv:1010.5822 (*cross-listing*) Date: Wed, 27 Oct 2010 22:59:17 GMT (3560kb,D) Title: Gauge Gravity: a forward-looking introduction Authors: Andrew Randono Categories: gr-qc hep-th math-ph math.MP Comments: 62 pages, 8 figures \\ This article is a review of modern approaches to gravity that treat the gravitational interaction as a type of gauge theory. The purpose of the article is twofold. First, it is written in a colloquial style and is intended to be a pedagogical introduction to the gauge approach to gravity. I begin with a review of the Einstein-Cartan formulation of gravity, move on to the Macdowell-Mansouri approach, then show how gravity can be viewed as the symmetry broken phase of an (A)dS-gauge theory. This covers roughly the first half of the article. Armed with these tools, the remainder of the article is geared toward new insights and new lines of research that can be gained by viewing gravity from this perspective. Drawing from familiar concepts from the symmetry broken gauge theories of the standard model, we show how the topological structure of the gauge group allows for an infinite class of new solutions to the Einstein-Cartan field equations that can be thought of as degenerate ground states of the theory. We argue that quantum mechanical tunneling allows for transitions between the degenerate vacua. Generalizing the tunneling process from a topological phase of the gauge theory to an arbitrary geometry leads to a modern reformulation of the Hartle-Hawking "no boundary" proposal. \\ ( http://arxiv.org/abs/1010.5822 , 3560kb) ------------------------------------------------------------------------------ \\ arXiv:1010.5831 (*cross-listing*) Date: Thu, 28 Oct 2010 00:47:02 GMT (12kb) Title: On spectral geometry approach to Horava-Lifshitz gravity: Spectral dimension Authors: A. Pinzul Categories: hep-th gr-qc math-ph math.MP \\ We initiate study of Horava-Lifshitz models of gravity in the framework of spectral geometry. As the first step, we calculate the dimension of space-time. It is shown, that for the natural choice of a Dirac operator (or rather corresponding generalized Laplacian), which respects both the foliation structure and anisotropic scaling, the result of Horava on spectral dimension is reproduced for an arbitrary, non-flat space-time. The advantage and further applications of our approach are discussed. \\ ( http://arxiv.org/abs/1010.5831 , 12kb) ------------------------------------------------------------------------------ \\ arXiv:1010.5973 (*cross-listing*) Date: Thu, 28 Oct 2010 14:04:43 GMT (960kb,D) Title: Domain walls and Schramm-Loewner evolution in the random-field Ising model Authors: Jacob D. Stevenson and Martin Weigel Categories: cond-mat.stat-mech cond-mat.dis-nn math-ph math.MP \\ The concept of Schramm-Loewner evolution provides a unified description of domain boundaries of many lattice spin systems in two dimensions, possibly even including systems with quenched disorder. Here, we study domain walls in the random-field Ising model. Although, in two dimensions, this system does not show an ordering transition to a ferromagnetic state, in the presence of a uniform external field spin domains percolate beyond a critical field strength. Using exact ground state calculations of very large systems, we examine ground state domain walls near this percolation transition finding strong evidence that they are conformally invariant and satisfy the domain Markov property, implying compatibility with Schramm-Loewner evolution (SLE_{\kappa}) with parameter \kappa = 6. These results might pave the way for new field-theoretic treatments of systems with quenched disorder. \\ ( http://arxiv.org/abs/1010.5973 , 960kb) ------------------------------------------------------------------------------ \\ arXiv:1010.6004 (*cross-listing*) Date: Thu, 28 Oct 2010 16:03:53 GMT (20kb) Title: Quantum Stochastic Dynamic and Quantum Measurement in Multi-Photon Optics Authors: Ricardo Castro Santis Categories: math.PR math-ph math.MP \\ In this work a generic model of \emph{multi-photon optics} is studied. It is considered $m$ pump and $n$ subharmonic fields. It shows how the multi-photon system, with direct and homodyne detection, can be obtained rigorously in the context of \emph{Measurement theory in Open Quantum System} (see \cite{Bar-OQS}, \cite{Bar-1990-QO} and \cite{RCS-LAP}). This is done trough the \emph{Quantum Stochastic Differential Equations} with unbounded coefficients (see \cite{Fagnola-Wills}, and \cite{RCS-LAP}). In particular the existence of the dynamics is proved, and a continuous measurements scheme is provided. \\ ( http://arxiv.org/abs/1010.6004 , 20kb) %%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%%--%% ------------------------------------------------------------------------------ \\ arXiv:0808.0112 (*cross-listing*) replaced with revised version Thu, 28 Oct 2010 10:28:03 GMT (33kb) Title: Mathematical Structure of Quantum Decision Theory Authors: V.I. Yukalov and D. Sornette Categories: cs.AI math-ph math.MP quant-ph Comments: 40 pages Journal-ref: Advances in Complex Systems 13, 659-698 (2010) \\ ( http://arxiv.org/abs/0808.0112 , 33kb) ------------------------------------------------------------------------------ \\ arXiv:1004.5387 replaced with revised version Thu, 28 Oct 2010 17:58:50 GMT (29kb) Title: On classification of Poisson vertex algebras Authors: Alberto De Sole, Victor Kac and Minoru Wakimoto Categories: math-ph math.MP Comments: paper replaced 10/28/10 \\ ( http://arxiv.org/abs/1004.5387 , 29kb) ------------------------------------------------------------------------------ \\ arXiv:1009.2005 (*cross-listing*) replaced with revised version Thu, 28 Oct 2010 06:17:33 GMT (87kb) Title: Continuous Dependence of Cauchy Problem For Nonlinear Schr\"{o}dinger Equation in $H^{s}$ Authors: Wei Dai, Weihua Yang and Daomin Cao Categories: math.AP math-ph math.MP Comments: 46pages, no figure MSC-class: 35Q55 \\ ( http://arxiv.org/abs/1009.2005 , 87kb) ------------------------------------------------------------------------------ \\ arXiv:1010.4829 (*cross-listing*) replaced with revised version Thu, 28 Oct 2010 03:56:56 GMT (6kb) Title: Distribution of the Riemann zeros represented by the Fermi gas Authors: Shigenori Tanaka Categories: quant-ph math-ph math.MP Comments: 7 pages MSC-class: 11Mxx \\ ( http://arxiv.org/abs/1010.4829 , 6kb) %%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%---%%%--- For subscribe options to combined physics archives, e-mail To: physics@arXiv.org, Subject: subscribe ----------------------------------------------------------------------------- For help on viewing and making submissions, see http://arXiv.org/help/ For a list of archive mirror sites, see http://arXiv.org/servers.html ----------------------------------------------------------------------------- Third-party submissions cause excessive problems. 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